A remark about the Connes fusion tensor product

Andreas Thom

We analyze the algebraic structure of the Connes fusion tensor product
(CFTP) in the case of bi-finite Hilbert modules over a von Neumann algebra
M. It turns out that all complications in its definition disappear if one
uses the closely related bi-modules of bounded vectors. We construct an
equivalence of monoidal categories with duality between a category of
Hilbert bi-modules over M with CFTP and some natural category of
bi-modules over M with the usual relative algebraic tensor product.